TITLE:
The Coordinate-Free Prediction in Finite Populations with Correlated Observations
AUTHORS:
Silvia N. Elian
KEYWORDS:
Coordinate-Free Models, Best Linear Unbiased Predictor, Covariance Matrix, Orthogonal Projection
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.2,
April
20,
2017
ABSTRACT: In this paper, we got the best linear unbiased predictor of any linear function of the elements of a finite population under coordinate-free models. The optimal predictor of these quantities was obtained in an earlier work considering models with a known diagonal covariance matrix. We extended this result assuming any known covariance matrix. It is shown that in the particular case of the coordinatized models, this general predictor coincides with the optimal predictor of the total population under a regression super population model with correlated observations.